Analysis of gradient algorithms for TLS-based adaptive IIR filters

IEEE Transactions on Signal Processing

Volumn 52, Issue 12, 2004, Pages 3345-3356

  Dunne, Bruce E ^a   Williamson, Geoffrey A ^b  

^a GRAND VALLEY STATE UNIVERSITY   (United States)

^b Illinois Institute of Technology   (United States)

Author keywords

Adaptive equalizers; Adaptive filters; IIR filters; Least squares; Total least squares

Indexed keywords

ADAPTIVE ALGORITHMS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; GRADIENT METHODS; IIR FILTERS; THEOREM PROVING;

ADAPTIVE EQUALIZERS; GRADIENT ALGORITHMS; TOTAL LEAST SQUARES;

ADAPTIVE FILTERING;

EID: 9744285097     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2004.837408     Document Type: Article

References (31)

1. L. J. Gleser, "Estimation in a multivariate 'Errors In Variables' regression model: Large sample results," Ann. Statist., vol. 9, no. 1, pp. 24-44, 1981.
2. S. Van Huffell and J. Vandewalle, The Total Least Squares Problem: Computational Aspects and Analysis, ser. Frontiers in Applied Mathematics. Philadelphia, PA: SIAM, 1991.
3. L. Xu, E. Oja, and C. Suen, "Modified Hebbian learning for curve and surface fitting," Neural Networks, vol. 5, no. 3, pp. 441-457, 1992.
4. A. Cichocki and R. Unbehauen, "Simplified neural networks for solving linear least squares and total least squares problems in real time," IEEE Trans. Neural Networks, vol. 5, pp. 910-923, Nov. 1994.
5. E. Oja and L. Wang, "Robust fitting by nonlinear neural units" Neural Networks, vol. 9, no. 3, pp. 435-444, 1996.
6. P. Comon and G. H. Golub, "Tracking a few extreme singular values and vectors in signal processing," Proc. IEEE, vol. 78, no. 8, pp. 1327-1343, Aug. 1990.
7. E. Oja, "Principle components, minor components, and linear neural networks," Neural Networks, vol. 5, no. 6, pp. 927-935, 1992.
8. L. Fa-Long and L. Yan-Da, "Real-time computation of the eigenvector corresponding to the smallest eigenvalue of a positive definite matrix," IEEE Trans. Circuits Syst. I, vol. 41, pp. 550-553, Aug. 1994.
9. F. Luo and R. Unbehauen, "A minor subspace analysis algorithm," IEEE Trans. Neural Networks, vol. 8, pp. 1149-1155, Sept. 1997.
10. J. P. Delmas and F. Alberge, "Asymptoric performance analysis of sub-space adaptive algorithms introduced in the neural network literature," IEEE Trans. Signal Processing, vol. 46, pp. 170-182, Jan. 1998.
11. B. Z. Feng, Z. Bao, and W. X. Shi, "Cross-correlation neural network models for the smallest singular component of general matrix," Signal Process., vol. 64, no. 3, Feb. 1998.
12. H. Sakai and K. Shimizu, "A new adaptive algorithm for minor component analysis," Signal Process., vol. 71, no. 3, Dec. 1998.
13. Q. F. Zhang and Y. W. Leung, "A class of learning algorithms for principal component analysis and minor component analysis," IEEE Trans. Neural Networks, vol. 11, pp. 200-204, Jan. 2000.
14. P. Regalia, "An unbiased equation error identifier and reduced-order approximations," IEEE Trans. Signal Processing, vol. 42, pp. 1397-1412, June 1994.
15. B. E. Dunne and G. A. Williamson, "QR based TLS and mixed LS-TLS algorithms with applications to adaptive IIR filtering," IEEE Trans. Signal Processing, vol. 51, pp. 386-394, Feb. 2003.
16. K. C. Ho and Y. T. Chan, "Bias removal in equation-error adaptive IIR filters," IEEE Trans. Signal Processing, vol. 43, pp. 51-62, Jan. 1995.
17. C. Davila, "An algorithm for efficient, unbiased, equation-error infinite impulse response adaptive filtering," IEEE Trans. Signal Processing, vol. 42, pp. 1221-1226, May 1994.
18. B. E. Dunne and G. A. Williamson, "A locally stable adaptive TLS algorithm," in Proc. 32nd Annu. Asilomar Conf., Pacific Grove, CA. Nov. 1998.
19. S. C. Douglas and M. C. Rupp, "On bias removal and unit norm constraints in equation error adaptive IIR filters," in Proc. 30th Asilomar Conf. Signals, Syst., Comput., vol. 2, Pacific Grove, CA. Oct. 1996, pp. 1093-1097.
20. M. Rupp and S. C. Douglas, "Deterministic stability analyzes of unit-norm constrained algorithms for unbiased adaptive IIR filtering," in Proc. ICASSP, 1997.
21. K. Gao, M. O. Ahmed, and M. N. S. Swamy, "A constrained anti-Hebbian learning algorithm for total least-squares estimation with application to adaptive FIR and IIR filtering," IEEE Trans. Circuits Syst. II vol. 41, pp. 718-729, Nov. 1994.
22. S. C. Douglas, "Analysis of an anti-Hebbian adaptive FIR filtering algorithm," IEEE Trans. Circuits Syst. II, vol. 43, pp. 777-780, Nov. 1996.
23. D.-Z. Feng, Z. Bao, and L.-C. Jiao, "Total least mean squares algorithm," IEEE Trans. Signal Processing, vol. 45, pp. 2122-2130, Aug. 1998.
24. H. C. So, "Least mean square algorithm for unbiased impulse response estimation," in Proc. 45th Midwest Symp. Circuits Syst., Tulsa, OK, Aug. 2002.
25. H.-N. Kim and W.-J. Song, "Unbiased equation-error adaptive IIR filtering based ou monic normalization," IEEE Signal Processing Lett., vol. 6, pp. 35-37, Feb. 1999.
26. B. Widrow and M. E. Hoff, "Adaptive switching circuits," in IRE WESCON Convention Rec., vol. 4, New York, 1960, pp. 96-104.
27. M. W. Hirsch and S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra. Orlando, FL: Academic, 1974.
28. B. N. Parlett, The Symmetric Eigenvalue Problem. Englewood Cliffs, N. J.: Prentice-Hall, 1980.
29. R. Mathias, "Quadratic residual bounds for the Hermitian eigenvalue problem," SIAM J. Matrix Anal. Appl., vol. 19, pp. 541-550, Apr. 1998.
30. P. Lancaster and M. Tismenetsky, The Theory of Matrices, Second ed. Orlando, FL: Academic, 1985, p. 188.
31. S. A. Hu and R. L. Smith, "The Schur complement interlacing theorem," SIAM J. Matrix Anal. Appl., vol. 16, no. 3, pp. 1013-1023, July 1995.